In Memoriam
William Warntz, 1922–1988
Donald G. Janelle
Department of Geography, University of Western Ontario
W
illiam Warntz was a pioneer in mathematical approaches to spatial analysis.
He attempted to bridge the divide between mathematics and the spatial representation of phenomena, leading to significant
contributions in theoretical geography. An untiring advocate of the systems view of geography, he
sought to identify principles of spatial organization that were common to phenomena in both
physical and human geography. He saw geography as a general science of locations, with descriptive geography describing locations, regional
geography classifying them, and theoretical geography predicting them. Mathematics was the key
to Bill’s early contributions. Indeed, before most
geographers were aware that it was occurring, he
had already published some of the classic papers
of the quantitative revolution. He also was an
avid scholar on the history of geographic thought
and devoted the later part of his career to identifying the origins of spatial analysis, including archival studies on the possible contributions of Sir
Isaac Newton to the development of geography
(1989).
Origins of a Spatial Scientist
William Warntz was born on October 10,1922,
in Berwick, Pennsylvania, in a coal mining area,
eighty miles up-river from Harrisburg, on the
Susquehanna. His father, Sterling Adrian Warntz,
was a superintendent in a local industry that
manufactured railway passenger cars, and his
mother, Lilian Grey Warntz, was a teacher. Bill
spent much of his boyhood playing baseball, practicing on the trombone, and reading, passions
that he nurtured throughout his life. At the dinner table, he would entertain his two sisters,
brother, and parents, asking question after question about geography and history, or posing geometrical puzzles for solution.
Education in liberal arts at Berwick School
(1936–1940) prepared him for undergraduate
work in economics. His education was interrupted, however, by six years in the U.S. Army Air
Force (1943–1948). In 1943, he entered the Aviation Cadet College Training Detachment at Albion College in Michigan, where he soloed in a
Piper Cub and played on the football team. This
was followed in 1943–1944 by a series of Air Force
flight and navigation schools that took him across
the country, studying cartography, meteorology,
and radio. Service as a navigator with the heavy
bombardment group in England earned him the
Purple Heart, three battle stars, and several other
Annals of the Association of American Geographers, 87(4), 1997, pp. 723–731
©1997 by Association of American Geographers
Published by Blackwell Publishers, 350 Main Street, Malden, MA 02148, and 108 Cowley Road, Oxford, OX4 1JF, UK.
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decorations. Injured in a crash landing of a B-24
that limped back to England after incurring damage from enemy fire, Warntz was stationed in
Cambridge for recuperation. This allowed frequent visits to Cambridge University, where his
fascination with the papers of Sir Isaac Newton
took his mind off the war and encouraged his
pursuit of educational goals.
Following the war, in 1946, Warntz was assigned to the Newfoundland Base Command for
duty in sea search-and-rescue missions. Events in
Newfoundland had lifelong personal and professional significance for him. In 1947 he met and
married A. Minerva Mosdell in Saint John’s.
Soulmates in their love of music, art, and history,
they had two children, Christopher and Pamela.
Interest in things geographical were heightened
by a fortuitous discovery of a book by John Q.
Stewart in the base library at Gander. In what
appeared to be a strange deviation from the principal theme of Coasts Waves and Weather, Stewart
(1945) applied Newton’s gravitational concept to
studying geographical patterns of population.
This insight set the stage for a lifelong friendship,
mentorship, and collaboration with Stewart, who
was at Princeton.
Warntz completed the B.S. in 1949, the A.M.
in 1951, and the Ph.D. in 1955, all three degrees
in economics from the University of Pennsylvania. Before the Ph.D., his curiosity for geographical questions arose independently of much formal
contact with geography. Recognizing this, he interrupted the Master’s program in economics (a
minor in geography) to take part in McGill University’s 1950 summer course in geography at
Stanstead, Quebec. Discussions there, with Kenneth Hare, Trevor Lloyd, Dudley Stamp, Edward
Ullman, and others stimulated questions about
the history of geography.
Although his Ph.D. was in economics, his thesis advisor was Lester E. Klimm, an economic and
military geographer, who became President of the
Association of American Geographers in 1958.
Warntz’s thesis on The Geography of Price involved thousands of calculations to derive population potential fields, all with a mechanical
adding machine.
An Engagement with Geography:
AGS and Princeton, 1956–1966
Warntz’s first academic position was as an instructor/assistant professor in Geography and
Economics at the University of Pennsylvania
(1949–1956). It was his appointment as research
associate and administrative assistant to the Director (Charles B. Hitchcock) of the American
Geographical Society in New York (1956–66),
however, that opened the engagement between
the broader community of geographers and his
imaginative mind. Among his published accomplishments while at AGS were Geography Now
and Then (1964), an insightful documentation of
the changing geography curricula in American
colleges from colonial days to the 1950s, and
two innovative books—Toward a Geography of
Price (1959), an extension of his dissertation,
and Macrogeography and Income Fronts (1965).
These books draw seemingly disparate interdisciplinary connections (meteorology, economics, and geography) and skillfully combine
cartography with mathematical constructs.
The latter book explains and predicts with uncanny accuracy the geographical patterns of
U.S. population and wealth through the last
decade of this century.
A less well-known achievement while at AGS
was a 200-hour spare-time construction of a
three-dimensional map showing population potential of the U.S.—a special AGS exhibit on
“New York: An International City” for the
1964–1965 New York World’s Fair (AGS 1964).
With patience and precision, he hammered more
than 3,000 nails (one for each county) onto a
board measuring 2 × 3.25 feet, in preparation for
a sculptor to cover with plaster. This outreach to
the public with geography was common in
Warntz’s career. He wrote articles for local newspapers, spoke before local geography societies,
prepared television seminars on an “Introduction
to Geography” (22 hours for WCAU in Philadelphia in 1964) and on “Geography, Concepts and
Applications” (13 hours for WHDH in Boston in
1968), and assisted local school boards and teachers with geography curricula.
During his time with AGS, Warntz lived with
his family in Princeton, New Jersey. In 1957, he
joined Stewart’s Social Physics Project as a research associate in the Department of AstroPhysical Sciences at Princeton. He was a frequent
visiting lecturer in Geography at Hunter College
and at Rutgers University, and in Regional Science at the University of Pennsylvania. In addition, he supervised two Ph.D. dissertations at
Columbia University (David Neft in Statistics
and Michael Woldenberg in Geography). The
daily commutes by train between New York and
William Warntz
Princeton were opportunities for reflection and
reading, and also time for drafting Geographers
and What They Do (1964), an introduction to the
discipline for school-age readers.
Jointly, Stewart and Warntz pioneered research on the population potential of the U.S. and
on general concepts of what Warntz described as
macrogeography. Their extensions of the gravity
model continue to serve the practical needs of
marketing researchers. This collaboration with
Stewart, the opportunities to take part in the
development of the regional science discipline,
and the experiences with the American Geographical Society were, for Warntz, possibly the
most enjoyable period of his career. He commented frequently about the joy of working with,
and his great respect for, his AGS associates—Charlie Hitchcock, Wilma Fairchild,
David Lowenthal, and Mait Miller.
The Harvard Years, 1966–1971
In 1966 Warntz became professor of Theoretical Geography and Regional Planning in Harvard
University’s Graduate School of Design (GSD)
and joined the research team in the Laboratory
for Computer Graphics. The Lab was set up by
Howard T. Fisher, the originator of SYMAP, one
of the first general computer-mapping programs,
with support from the Ford Foundation. Warntz’s
appointment was intended to provide strong intellectual grounding for the uses of SYMAP. He
covered most of his salary with funding that he
brought with him from New York—an Office of
Naval Research grant for work on “Geography
and the Properties of Surfaces.” Warntz helped to
define the lab’s mission by appending the phrase
“and Spatial Analysis.” He was appointed Director of LCG&SA in 1968. Though not disposed to
programming computers, his leadership there influenced some of the major developments in computerized cartography. With significant support
from the National Science Foundation and from
the Office of Naval Research, Warntz attracted a
range of young mathematicians, geographers, and
planners who held in common a certain fascination for things spatial. His courses (Regional Resources Planning, and Theory of the Region) were
springboards for student research. He set them
loose on a host of theoretical problems centered
on the Sandwich Theorem, Thiessen polygons,
minimum-path algorithms, topologies of surfaces, map projections, and morphologies of
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branching systems. Many of his younger associates and students at Harvard are now major contributors to developments in geographic
information systems (GIS) (for example, Roger
Dangermond).
Located in the basement of Memorial Hall, in
an area once occupied by B. F. Skinner’s behavioral-science pigeon coop, the Laboratory for
Computer Graphics and Spatial Analysis became
a center of innovation. Students had ready access
to his cardboard boxes, piled deep with the latest
papers from Brian Berry, Leslie Curry, Michael
Dacey, Bill Bunge, Peter Gould, Walter Isard,
Gunnar Olsson, and Waldo Tobler, among others.
Serendipitous insights flowed from frequent, informal and, usually, enthusiastic rap sessions,
punctuated by occasional musical jams, with Bill
on the tuba, Lance Benson on dulcimer, Geoffrey
Dutton on concertina, and Mike Woldenberg on
guitar.
Warntz introduced and edited the important
Harvard Papers in Theoretical Geography
(1966–1971). He and his colleagues published
imaginative work in this series, including lengthy
monographs on map projections, and applications of topological theorems and field quantity
theory. His trinity of “Geography, Geometry, and
Graphics” attained its most pronounced developments while at Harvard. True to his historical
interests, he drew inspiration from early Egyptian
and Greek scholars, searching for precedents of
spatial order. The Harvard Papers in Theoretical
Geography highlight research on the properties of
surfaces, including topological relations, minimum cost paths, spatial hierarchies, and map
projections. Breakthroughs in Geography (1971a,
with Peter Wolff) provides a readable and popular
focus on these develpments, with related excerpts
from the writings of Ptolemy, Halley, Galton, von
Thünen, Horton and other contributors to the
integration of geography, geometry, and graphics.
Warntz thoroughly enjoyed his time with students at Harvard, but the politics of campus life
in the charged atomosphere of the late sixties had
its toll. He attempted to rekindle geography
within the university curricula, but with no positive outcome. In 1968 he was requested by Franklin Ford, Dean of the Faculty of Arts and Sciences,
to form an ad hoc committee to review the position of geography in the curriculum for possible
recommendations to the Committee on Educational Policy.
With prospects of establishing geography as a
full-status academic unit within Harvard College,
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Warntz anchored the intellectual foundations of
this initiative to the research underway in
LCG&SA. He envisioned a strong focus on theoretical geography as a science of locations, and
sought financial support from the National Science Foundation and from the Carnegie Corporation of New York. These carefully argued bids
were not successful, but a more serious obstacle
was the changing state of Ford’s health and his
resignation as Dean. This altered the dynamic,
but even more damaging was emerging turmoil in
the financial and intellectual health of the Graduate School of Design. Events quickly overshadowed the prospects for a geography program; they
e ve n t h re a te n e d s u stai n ed su ppo r t fo r
LCG&SA—what under the circumstances may
have been seen as an expensive luxury, and the
significance of which to both geography and science was not yet fully appreciated. This was not
so much an academic war over geography, as
Smith (1987) described the elimination of geography at Harvard in 1948. It was a war within
GSD, with prospects for geography’s renewed
presence diminished as a result.
Even though he held the position of a full
professor and had achieved significant success as
a teacher and researcher, Warntz’s appointments
at Harvard were contractual, and, as noted earlier, he funded much of his salary from research
grants. With increasingly discouraging prospects
for tenure status and little hope for introducing a
geography program, and before completing the
third of his three-year contracts, Warntz resigned
his position at Harvard in June 1971. Nonetheless, his dream of geography at Harvard persisted,
and, even long after his departure, he continued
to petition Ford’s successor, John T. Dunlop, and
President Derek C. Bok to bring the matter of
geography before the Committee on Educational
Policy.
Life in a Real Geography
Department: Western Ontario,
1971–1988
Warntz accepted an invitation to chair the
Department of Geography at the University of
Western Ontario in 1971, a position he held to
1976. Western’s Geography Department was
large by North American standards. It had more
than twenty-five full-time faculty, up to sixty
graduate students in residence, and between two
hundred to three hundred undergraduates majoring in geography. He expected to find a community of nearly four hundred aficionados of
theoretical geography. Indeed, an indisputable
champion of theoretical geography, William
Bunge, was a visiting professor in the first year of
Warntz’s tenure at Western. Allen Philbrick,
noted for his work on areal functional organization and for creation of original map projections,
provided a critical but sympathetic comrade for
Warntz. And a number of young geographers with
interest in spatial analysis were beginning their
academic careers at Western (e.g., Michael Goodchild, Donald Janelle, Terence R. Smith, and
Roger White), offering Warntz an obliging audience for expansive thinking. But, as with most
departments across North America, theoretical
geography and spatial analysis shared ground at
Western with other important disciplinary viewpoints. A diverse range of faculty interests paralleled the discipline’s eclectic reality. To Warntz,
this was symptomatic of a lack of disciplinary
focus and offered a rationale for invoking a systems perspective—spatial systems theory.
As is true for most academics, Warntz achieved
partial success in reaching his ideal, but mostly
through students attracted to his research and
academic style, particularly his Ph.D. advisees
William J. Coffey and James A. Pooler. At Western, Warntz taught undergraduate courses on the
Geography of the U.S., Maps—Their Makers and
Their Uses, Intermediate Theoretical Geography, and the required Honors Seminar on Geographical Thought. At the graduate level, courses
on Spatial Concepts and Spatial Analysis and on
Macrogeographic Systems and Environmental
Quality, were central to the programs of many
students.
Hallmarks of academic life at Western, however, were Warntz’s frequent research seminars on
his latest findings. Presentations usually lasted for
two hours, at least, and always attracted more
students and faculty than the room could hold.
With reams of overhead transparencies, dry wit,
and total command of his subject, Warntz explored themes on cartographic solutions to problems in location theory, cultural literacy and the
knowledge of place names, innovative and peaceful spaces, multidimensional scaling of geography’s ivory tower, and others. His famous “peaks,
pits, passes and pales, course lines and ridge lines,
hills, and dales” approach to analyzing topographical surfaces was not only applied to the
socioeconomic terrain of the U.S., Canada, and
William Warntz
the world, but was also used to explore properties
of physical landscapes and meteorological pressure patterns. Not surprisingly, Warntz reigned
supreme in the Department’s annual Christmas
Orals (geographical trivia quiz)—dreaming up
geographical questions that stumped most and
drawing on a wealth of knowledge for quick responses to the most obscure questions that his
colleagues and students could imagine. It didn’t
seem fair.
In moving to London, Ontario, Bill and Minerva kept “Wendling,” their lovely home in Andover, Massachusetts. It became a holiday refuge
from the mounting responsibilities of a department chair in periods of growing economic uncertainty, and a place to pursue his writing. Asked
where he lived, he described his “weighted mean
residential location” as Syracuse, New York, approximately midway between London and Andover. Wendling was also a vantage point on
continuing developments at Harvard, and, following 1983, it gave him a base to participate as
a Research Scholar in Harvard’s Center for Population Studies, where he was investigating population patterns in rural Europe in the thirteenth
to eighteenth centuries.
At Western, Warntz developed the Macrogeographic Systems Research Workshop, devoted
to studying the growth of the North American
economic system and global patterns in physical
geography. This workshop was also the springboard for further developments in spatial analysis
and computer cartography. Through the affiliation and initiatives of Michael Goodchild, David
Mark, and many students, the workshop was
transformed from its exclusive focus on macrogeography into a major contributor to the foundations of GIS. Macrogeography remained a
dominant theme in Warntz’s work through 1978,
culminating with his presentation of “Canada: Its
Geographical Unity and Diversity” to the prestigious Royal Society of Canada. Afterwards, the
history of geography and its contemporary role in
society marked the foci of his research. He enjoyed spending summers and sabbaticals at Cambridge University, researching the geographical
contributions of Isaac Newton and Bernhard
Varenius. His last published paper, based largely
on archival work at Cambridge, appeared following his death. This paper shows his capacity to
shed light on contemporary themes in geography
through studies of the past. “Newton, the Newtonians, and the Geographia Generalis Varenii”
(1989) is only a fragment of his intended project,
727
but ranks as a significant contribution to the
history of geographic thought. In preparing for
this project, he learned Latin in order to translate
Newton’s editions of Varenius.
Retrospective
Bill Warntz received many honors: President
of the International Regional Science Association (1965–1966), Fellow of the American Association for the Advancement of Science, Fellow
of the American Geographical Society, Fellow of
the Explorers Club of New York City, Life Associate of Clare Hall (Cambridge University), and
Fellow of the Royal Society of Canada. Unpublished books, research analyses, and correspondence are in the Warntz Collection of the
Regional Science Archives at Cornell University.
A book-length manuscript, “Distances in the
Man-made Environment,” completed in 1971,
follows the geometric tradition of spatial analysis.
Another unpublished book, finished in his final
weeks at the hospital (with Jane Forsythe), “Place
Names, Probabilities, and Priorities,” attempts to
position geographical literacy in a broad intellectual framework. These manuscripts join yet another unpublished book—“Geography: The
Innocent Science.” Jointly authored with William
Bunge in the 1960s, this work explores the primitive mathematical and geometrical base of physical and human phenomena. Warntz had saved
much work for publication after retirement but
died on 29 May 1988, less than six weeks before
retirement. Work in progress included original
documentation on the geographical spread of
printing and the origins of universities in Europe,
urban and rural population distributions in
Europe in 1200–1700 A.D., a series of essays on
geographical puzzles and paradoxes, a philosophical history of ideas on the shape of the earth, and
studies on the contemporary role of universities
in North America.
A festschrift from associates and students (Coffey 1988) marks Warntz’s intellectual influence
on discourse in Geography. He had a knack for
unleashing the creativity of students; he regarded
them as colleagues and delighted in exchanges on
almost any subject. For those of us who knew and
worked closely with Warntz, he had a formidable
intellectual presence. He was noted for his quick
mind and for his ability to call upon an astounding
range of theory and facts, but was also warm and
generous.
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Though Warntz’s lasting contributions are in
scholarship, friends recall his accomplishments as
a gifted musician and as a fierce competitor in
squash and tennis. Other diversions included an
encyclopedic knowledge of baseball and an insatiable addiction to geographical puzzles, paradoxes, and algorithms. He read widely in
astronomy, cartography, mathematics, the history of exploration, and the history of education.
He combined a sense of history and social structure with insights from mathematics, economics,
and meteorology to produce tantalizing research
about geographical patterns. His curiosity and
enthusiasm opened the minds of many students
and colleagues. Classroom and conversation queries, such as, “How wide is the Pacific Ocean from
Panama City to Shanghai?” marked a constant
engagement with ideas and challenges to anyone
who ever spent more than a few minutes with
him. The rigor of a specialist and the breadth of
a generalist mark William Warntz as one of geography’s outstanding personalities in the twentieth
century.
Warntz’s views on the discipline were seen as
unusual in the early days of the quantitative
revolution. He departed from the established
dogmas on geography but pursued his curiositydriven questions in search of underlying truths
that might unite an approach to human and
physical phenomena. Although his papers appeared regularly in the prestigious Geographical
Review, Warntz was seen by many as separated
from the discipline’s mainstream—educated in
economics, never holding an academic post in a
major geography department until the last third
of his career, and never maintaining active membership in geography’s professional and scholarly
associations. His loyalty was to geography and to
a life of the mind; he found his intellectual home
in the realm of regional science, systems theory,
computer graphics, and mathematical topology.
The interdisciplinary nature of his work won respect among mathematicians, physicists, and
economists. Within geography, spatial analysts
and economic geographers identified most readily
with his approach, and current-day geographical
information scientists appreciate his important
role in meshing theory with often elegant empirical demonstrations and in mentoring some of
today’s leaders in GIS.
By the 1970s, Warntz’s work was often cited for
its excesses of analogy between human and physical systems, and he was frequently cast as the
archetypal scientific positivist. This shift in philo-
sophical grounding for geography was recognized
by Warntz and may account, in part, for the
reorientation of research objectives in the latter
part of his career, and for the many unpublished
manuscripts found buried in boxes of computer
output, notes, and correspondence. As he turned
towards new intellectual challenges regarding the
history of the discipline before the nineteenth
century, and to questions about contemporary
education in geography, he never lost sight of
his roots in spatial analysis, puzzles, music, and
baseball.
Acknowledgments
This memorial essay is derived from the insights of
William Warntz’s close associates and friends. I borrowed freely from correspondence and other materials
that are now found in the Warntz Collection of the
Regional Science Archives, Department of Manuscripts and University Archives, Cornell University,
Ithaca, NY 14853. Special appreciation is extended to
Patricia Chalk, William Coffey, Geoffrey Dutton, Judy
Bowley, Michael Goodchild, David Mark, Waldo
Tobler, and Michael Woldenberg. Warntz’s sister, Maxine Smeltzer of Concord, New Hampshire, provided
details on his early childhood interests. I hold full
responsibility for lateness in the appearance of this
essay, approved by the Council of the Association of
American Geographers in November 1988.
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1971e The Sandwich Theorem—A Basic One for
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1973b First Variations on the Theme, Cartographics
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1981
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Correspondence: Department of Geography, University of Western Ontario, London, Canada N6A 5C2; email
Janelle@sscl.uwo.ca.